微积分的发展及意义

微积分的发展及意义

微积分，作为数学的代名词，其错误的概念被广而周知。实际上，数学分析包括微积分、函数论等许多分支学科，它只是数学中的其中一个组成部分。我们现在一般习惯于把数学分析和微积分等同起来，数学分析成了微积分的同义词，而微积分的基本概念和内容包括微分学和积分学。

微积分是研究函数的微分、积分以及有关概念和应用的数学分支。微积分是微分学和积分学的统称，微积分是建立在实数、函数和极限的基础上的。

它的萌芽、发生与发展经历了漫长的时期。公元前三世纪，古希腊的阿基米德在研究解决抛物弓形的面积、球和球冠面积、螺线下面积和旋转双曲体的体积的问题中，就隐含着近代积分学的思想。到了十七世纪，有许多科学问题需要解决，这些问题也就成了促使微积分产生的因素。归结起来，大约有四种主要类型的问题：第一类是研究运动的时候直接出现的，也就是求即时速度的问题。第二类问题是求曲线的切线的问题。第三类问题是求函数的最大值和最小值问题。第四类问题是求曲线长、曲线围成的面积、曲面围成的体积、物体的重心、一个体积相当大的物体作用于另一物体上的引力。终于在十七世纪下半叶，在前人工作的基础上，英国大科学家牛顿和德国数学家莱布尼茨建立了微积分，但是还没有建立完整健全的理论体系，直到19世纪初，以柯西为首的科学家们，对微积分的理论进行了认真研究，

建立了极限理论，后来又经过德国数学家维尔斯特拉斯进一步的严格化，使极限理论成为了微积分的坚定基础。随后微积分才开始了其真正的发展之路。

微积分的产生是数学上的伟大创造。它从生产技术和理论科学的需要中产生，又反过来广泛影响着生产技术和科学的发展。如今，微积分已是广大科学工作者以及技术人员不可缺少的工具。微积分是与应用联系着发展起来的，在形成之初和后来，微积分学极大的推动了数学的发展，同时也极大的推动了物理学、化学、生物学、工程学、经济学等的发展。并在这些学科中有越来越广泛的应用，特别是计算机的出现更有助于这些应用的不断发展。并且在我们的生活中，微积分的应用也不少见，例如，计算在建造一水池，原材料的最省的方法及其价格最优的方法等等。

根据上文所述，我们应该多了解微积分的知识与应用，尤其是能够学以致用，只有这样，我们才能更好的生活与工作。

外国语学院

0905106-11

张露露

the Development and Significance of Calculus Calculus, being as an equivalent of mathematicals, always has its wrong definition in most people's eyes. As the matter of fact, mathematical analysis includes calculus, functions and many other branches of the discipline. Nowadays we are used to equating mathematical analysis with calculus which is the synonym of that. The basic concept of calculus involves in two : differential calculus and integral calculus.

Calculus is a branch of mathematicals, researching functions of the differential, integral and relevant concepts and applications, which is based on real numbers, functions and limit.

Calculus, owning its bud, generation and development, has experienced a long period. In 3rd century BC, Archimedes in ancient Greece solved the problems of parabolic bow area and the volume of rotating hyperbolic body and so on, implying the ideas of modern calculus. When came to 17th century, many scientific problems are ready to be tackled, which brought its incentives to the appearance of calculus. To sum up, there are four main types: the first is to study movement directly seeking real-time speed;The second problem the curve of tangent; The third category the maximum and minimum values of functions; The fourth problem curve length, area and volume curve enclosed, the center of gravity, and effect of a considerable volume of the object pulling on another object. Then in the second half of the 17th century, on the basis of previous work, the

great British scientist Newton and German mathematician Leibniz built up calculus, being viewed as preliminary job. Until the early 19th century, the French Scientific Institute of scientists led by the Cauchy established the limit theory, and later after the German mathematician Weierstrass further standardization of limit theory, a firm foundation for the calculus, it paved the way for the further development of the calculus.

Being a great wonder in the history of mathematicals, calculus comes from the needs of production technology and theoretical science, and in turn widely exert influence on them. Today, the calculus is an indispensable tool for the majority of scientists and technical personnel. Calculus is associated with applications. Not only at the beginning of foundation, but also afterwards calculus greatly promoted the development of mathematics, along with enhancing improvements of the various branches of physics, chemistry, biology, engineering, economics especially doing more contribute to continuous development of these applications because of emergence of the computer. Even in our daily life, we can see the wide application of calculus, like finding out the best way of minimum materials used and the optimal method of the least amount of money devoted when building a pool, and so on.

As discussed above, there is a must for us to have a better understanding of the knowledge of calculus. What's more, only after turning theories into practices can we feel better in life and at work.